BRO CAN SOMEONE PLEASE HELP ME
2 answers:
You might be interested in
Answer:
option: B () is correct.
Step-by-step explanation:
We are given the solution set as seen from the graph as:
(-4,2)
1)
On solving the first inequality we have:
On using the method of splitting the middle term we have:
⇒
⇒
And we know that the product of two quantities are negative if either one of them is negative so we have two cases:
case 1:
and
i.e. x>-2 and x<4
so we have the region as:
(-2,4)
Case 2:
and
i.e. x<-2 and x>4
Hence, we did not get a common region.
Hence from both the cases we did not get the required region.
Hence, option 1 is incorrect.
2)
We are given the second inequality as:
On using the method of splitting the middle term we have:
⇒
⇒
And we know that the product of two quantities are negative if either one of them is negative so we have two cases:
case 1:
and
i.e. x>2 and x<-4
Hence, we do not get a common region.
Case 2:
and
i.e. x<2 and x>-4
Hence the common region is (-4,2) which is same as the given option.
Hence, option B is correct.
3)
On using the method of splitting the middle term we have:
⇒
⇒
And we know that the product of two quantities are positive if either both of them are negative or both of them are positive so we have two cases:
Case 1:
and
i.e. x>-2 and x>4
Hence, the common region is (4,∞)
Case 2:
and
i.e. x<-2 and x<4
Hence, the common region is: (-∞,-2)
Hence, from both the cases we did not get the desired answer.
Hence, option C is incorrect.
4)
On using the method of splitting the middle term we have:
⇒
⇒
And we know that the product of two quantities are positive if either both of them are negative or both of them are positive so we have two cases:
Case 1:
and
i.e. x<2 and x<-4
Hence, the common region is: (-∞,-4)
Case 2:
and
i.e. x>2 and x>-4.
Hence, the common region is: (2,∞)
Hence from both the case we do not have the desired region.
Hence, option D is incorrect.
Answer:
A. 13.9 and 14.1 inches
See explanation below.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the outside diameters of a population, and for this case we know the distribution for X is given by:
Where and
If we want the middle 68% of the data we need to have on the tails 16% on each one
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.16 of the area on the left and 0.84 of the area on the right it's z=-0.994. On this case P(Z<-0.994)=0.16 and P(z>-0.994)=0.84
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
And since the distribution is symmetrical for the upper limit we can use z = 0.994 and we have:
And if we solve for a we got
So the correct answer for this case would be:
A. 13.9 and 14.1 inches